This regular 4-d polytope is made of 600 tetrahedral unit cells. It is rotating in hyperspace, continually changing the three-dimensional “slice” of it which you can see. The software used to make this image may be purchased, or tried for free, at http://www.software3d.com/Stella.php.
The software used to make this is available as a free trial download at http://www.software3d.com/stella.php.
I made this .gif with Stella 4d, software available as a free trial download at http://www.software3d.com/stella.php.
What do Carl Sagan, Richard Feynman, and Natalie Portman have in common?
They all have the same Erdős-Bacon number: six.
Natalie Portman collaborated (as Natalie Hershlag) with Abigail A. Baird, who wrote mathematical papers in a further collaborative path which leads to Joseph Gillis. Gillis, having co-written a paper with Paul Erdős himself, has an Erdős number of one. This gives Portman an Erdös number of five. Bacon and Portman both appear a movie (which one? See the details in this Wikipedia article: http://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Bacon_number), which gives Portman a Bacon number of one.
The Erdős-Bacon number is simply the sum of these two numbers — hence Natalie Portman’s six: five plus one.
Feynman’s and Sagan’s sixes are more balanced. Richard Feynman’s is the most so, since his Erdős and Bacon numbers are both three.
I haven’t been able to determine who first thought of an Erdős-Bacon number, but . . . wow. It came from the blogosphere (Where else?) — Wikipedia reveals that much.
Some blogger might be obsessive enough, someday, to exhaustively determine exactly how many people even have such numbers. However, that person will not be me.
If oriented just right, ten rhombicosidodecahedra can be stuck together to form a regular decagonal ring.
You may try the software I used to make this, as a free trial download, at http://www.software3d.com/stella.php.
Software credit: http://www.software3d.com/stella.php
Seven snub cubes almost make a perfect ring. There’s a small region of overlap between two of them which precludes perfection in this case. If you click on the image, it will rotate, and you’ll be able to spot this overlap-region more easily.
Software credit: see http://www.software3d.com/stella.php
It’s made of metabidiminished rhombicosidodecahedra, and can be continued indefinitely.
Software credit, for the program used to create this .gif: see http://www.software3d.com/Stella.php for download and trial demo.
RobertLovesPi.net 